Conventional laser cavity design techniques contemplate a resonator cavity, shown in FIG. 1, comprising two reflecting elements 110 and 112, surrounding a gain medium 111. The gain medium can be a plasma, a gas, a liquid, or a solid (e.g., a crystal or a semiconductor). The gain medium is excited by a power source.
The term "laser" as used in this discussion is meant to be inclusive of stimulated emission oscillators of electromagnetic radiation of any frequency from radio-frequency (RF) to beyond x-ray frequencies. (RF lasers are sometimes called "masers" by others.) The laser beam will have one or more "modes". A mode in this discussion refers to a "spatial mode", also called a "spatial eigenmode". The mode, a characteristic of the laser beam, is created within a laser cavity and has both a power-distribution profile and a phase-distribution profile. These mode profiles are generally expressed in dimensions transverse to the direction of propagation of the laser beam. A spatial mode is to be distinguished from a "temporal mode", which describes the frequency characteristics of the laser beam. A "fundamental mode" is the spatial mode which has the least loss. Amplitude profile 114 of FIG. 1 illustrates a Gaussian fundamental mode versus transverse beam radius .rho.. Amplitude profile 115 of FIG. 1 also illustrates a Gaussian fundamental mode along with a second-order mode shown by curves 116 and 117.
The term "complex" as used in this discussion is mean numbers or functions having real and/or imaginary components.
The term "modal discrimination" describes a function of a laser resonator which can simultaneously provide a small fundamental-mode loss while providing large losses for higher-order modes. The modal discrimination is influenced by the chosen fundamental-mode shape, the length of the cavity, and the placement of aperture stops.
Recently, mode-selecting phase-conjugating mirrors have been used to establish tailored profiles for fundamental modes in CO.sub.2 lasers. U.S. Pat. No. 5,255,283 by Belanger teaches a circular mode-selecting phase-conjugating mirror used to establish a radially-tailored circularly-symmetric profile for a fundamental mode in a laser resonator.
The above prior art does not appear to teach how to design or fabricate a custom phase-conjugation mirror (CPCM) which will accommodate a fundamental-mode beam profile of arbitrary profile in Cartesian X and Y transverse dimensions.